Integrable models for shallow water with energy dependent spectral problems
Exactly Solvable and Integrable Systems
2013-05-02 v1
Abstract
We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependance on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup-Bousinesq equation. We formulate the inverse problem as a Riemann-Hilbert problem with a Z2 reduction group. The soliton solutions are explicitly obtained.
Keywords
Cite
@article{arxiv.1211.5567,
title = {Integrable models for shallow water with energy dependent spectral problems},
author = {Rossen I. Ivanov and Tony Lyons},
journal= {arXiv preprint arXiv:1211.5567},
year = {2013}
}
Comments
17 pages, 3 figures